Quantum Gross-Pitaevskii Equation
作者： J. Ignacio Cirac , Frank Verstraete , Frank Verstraete , Jutho Haegeman , Tobias J. Osborne
DOI: 10.21468/SCIPOSTPHYS.3.1.006
关键词:
摘要: We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and liquids. This is obtained by applying time-dependent variational principle to manifold continuous matrix product states. allows full description many body system - including entanglement correlations-and thus extends significantly beyond usual mean-field equation, which known fail (quasi) systems. By linearizing around stationary solution, we furthermore derive an associated Bogoliubov de Gennes equations. framework applied compute steady state response amplitude periodic perturbation potential.
scipost.org
mpg.de
harvard.edu
arxiv.org 
sci-hub.st 参考文章(63)
Mark J. Ablowitz, Nonlinear Dispersive Waves: Asymptotic Analysis and Solitons Cambridge University Press. ,(2011) , 10.1017/CBO9780511998324
Vladimir S. Buslaev, Catherine Sulem, On asymptotic stability of solitary waves for nonlinear Schrödinger equations Annales De L Institut Henri Poincare-analyse Non Lineaire. ,vol. 20, pp. 419- 475 ,(2003) , 10.1016/S0294-1449(02)00018-5
Jutho Haegeman, Christian Lubich, Ivan Oseledets, Bart Vandereycken, Frank Verstraete, Unifying time evolution and optimization with matrix product states Physical Review B. ,vol. 94, pp. 165116- ,(2016) , 10.1103/PHYSREVB.94.165116
F. Meinert, M. Panfil, M. J. Mark, K. Lauber, J.-S. Caux, H.-C. Nägerl, Probing the Excitations of a Lieb-Liniger Gas from Weak to Strong Coupling. Physical Review Letters. ,vol. 115, pp. 085301- 085301 ,(2015) , 10.1103/PHYSREVLETT.115.085301
Elliott H. Lieb, Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum Physical Review. ,vol. 130, pp. 1616- 1624 ,(1963) , 10.1103/PHYSREV.130.1616
David Cohen, Ernst Hairer, Christian Lubich, Conservation of energy, momentum and actions in numerical discretizations of non-linear wave equations Numerische Mathematik. ,vol. 110, pp. 113- 143 ,(2008) , 10.1007/S00211-008-0163-9
Jutho Haegeman, J. Ignacio Cirac, Tobias J. Osborne, Iztok Pižorn, Henri Verschelde, Frank Verstraete, Time-dependent variational principle for quantum lattices. Physical Review Letters. ,vol. 107, pp. 070601- 070601 ,(2011) , 10.1103/PHYSREVLETT.107.070601
Eugene P. Gross, Hydrodynamics of a Superfluid Condensate Journal of Mathematical Physics. ,vol. 4, pp. 195- 207 ,(1963) , 10.1063/1.1703944
Jun'ichi Ieda, Takahiko Miyakawa, Miki Wadati, Exact analysis of soliton dynamics in spinor Bose-Einstein condensates. Physical Review Letters. ,vol. 93, pp. 194102- ,(2004) , 10.1103/PHYSREVLETT.93.194102
Tobias J. Osborne, Jens Eisert, Frank Verstraete, Holographic quantum states. Physical Review Letters. ,vol. 105, pp. 260401- 260401 ,(2010) , 10.1103/PHYSREVLETT.105.260401